`a. =\frac{5(x-y)(x+y)}{1[-(x-y)]^2(x+y)}`
`= \frac{5(x-y)}{11(x-y)^2}`
`= \frac{5}{11(x-y)}`
`b. =\frac{4x^2y^2-4xy+1}{8x^3y^3-1-12x^2y^2+6xy}`
`= \frac{(2xy-1)^2}{(2xy-1)(4x^2y^2+2xy+1)-6xy(2xy-1)}`
`= \frac{(2xy-1)^2}{(2xy-1)(4x^2y^2+2xy+1-6xy)}`
`= \frac{(2xy-1)^2}{(2xy-1)(4x^2y^2-4xy+1)}`
`= \frac{2xy-1}{4x^2y^2-4xy+1}`
`= \frac{2xy-1}{(2xy-1)^2}`
`= \frac{1}{2xy-1}`
`c. =\frac{(x+2)(x+1)(x-5)(x+5)}{(x+5)(x+2)}`
`= (x+1)(x-5)`
`= x^2-4x-5`
`d. =\frac{(x^3-y^3)(x^3+y^3)}{(x^2-y^2)(x^2+y^2)-xy(x^2-y^2)}`
`= \frac{(x-y)(x^2+xy+y^2)(x+y)(x^2-xy+y^2)}{(x-y)(x+y)(x^2+y^2)-xy(x-y)(x+y)}`
`= \frac{(x-y)(x^2+xy+y^2)(x+y)(x^2-xy+y^2)}{(x-y)(x+y)[(x^2+y^2)-xy]}`
`= x^2+xy+y^2`
